Frequency-modulated atomic force microscopy operation by imaging at the frequency shift minimum: The dip-df mode

(1)

Frequency-modulated atomic force microscopy operation by imaging at the frequency shift minimum: The dip-df mode

Sebastian Rode, Martin Schreiber Philipp Rahe

Citation: Review of Scientific Instruments 85, 043707 (2014); doi: 10.1063/1.4871436 View online: http://dx.doi.org/10.1063/1.4871436

View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/4?ver=pdfcov Published by the AIP Publishing

Articles you may be interested in

Modification of a commercial atomic force microscopy for low-noise, high-resolution frequency-modulation imaging in liquid environment

Rev. Sci. Instrum. 82, 073703 (2011); 10.1063/1.3606399

Combined normal and torsional mode in frequency-modulation atomic force microscopy for lateral dissipation measurement

Appl. Phys. Lett. 88, 153112 (2006); 10.1063/1.2194367

Higher harmonics imaging in tapping-mode atomic-force microscopy Rev. Sci. Instrum. 74, 5111 (2003); 10.1063/1.1626008

A direct method to calculate tip–sample forces from frequency shifts in frequency-modulation atomic force microscopy

Appl. Phys. Lett. 78, 123 (2001); 10.1063/1.1335546

Rapid imaging of calcite crystal growth using atomic force microscopy with small cantilevers Appl. Phys. Lett. 73, 1658 (1998); 10.1063/1.122237

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

(2)

Frequency-modulated atomic force microscopy operation by imaging at the frequency shift minimum: The dip-df mode

Sebastian Rode,^a)Martin Schreiber,^b)Angelika Kühnle,^b)and Philipp Rahe^c) Institut für Physikalische Chemie, Fachbereich Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55099 Mainz, Germany

(Received 22 November 2013; accepted 3 April 2014; published online 28 April 2014)

In frequency modulated non-contact atomic force microscopy, the change of the cantilever frequency (f) is used as the input signal for the topography feedback loop. Around thef(z) minimum, however, stable feedback operation is challenging using a standard proportional-integral-derivative (PID) feedback design due to the change of sign in the slope. When operated under liquid conditions, it is furthermore difficult to address the attractive interaction regime due to its often moderate peakedness. Additionally, thefsignal level changes severely with time in this environment due to drift of the cantilever frequencyf0and, thus, requires constant adjustment. Here, we present an approach overcoming these obstacles by using the derivative offwith respect tozas the input signal for the topography feedback loop. Rather than regulating the absolute value to a preset setpoint, the slope of thefwith respect to zis regulated to zero. This new measurement mode not only makes the minimum of the f(z) curve directly accessible, but it also benefits from greatly increased opera- tion stability due to its immunity againstf₀ drift. We present isosurfaces of the f minimum acquired on the calcite CaCO₃(1014) surface in liquid environment, demonstrating the capability of our method to image in the attractive tip-sample interaction regime.© 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4871436]

I. INTRODUCTION

Over the last decades, atomic force microscopy (AFM) has proven to be one of the most useful techniques for resolv- ing surface structures from the mesoscopic scale down to the atomic level in fields such as surface science, biochemistry, or materials science.¹ Especially in the frequency-modulated (FM) non-contact (NC) mode, atomic resolution is nowa- days routinely achieved when operating the AFM under ultra- high vacuum conditions.² Recently, the success of atomic- scale imaging has been transferred to the liquid environment,³ demonstrating atomic-resolution imaging on surfaces such as, e.g., mica(001),⁴calcite(104),^5–8aragonite(001),⁹calcium difluorite¹⁰as well as LiNbO3(001),¹¹and, furthermore, high- resolution imaging on molecular systems.¹²

These achievements have only been possible after care- fully optimizing the experimental setup for increasing the signal-to-noise ratio.^3,13However, operating FM NC-AFM in liquid environment still requires a delicate adjustment of the scanning parameters compared to other AFM modes in different environments. Here we note that, first, usually large drift not only distorts the acquired images in all three spa- tial directions,¹⁴ but additionally causes a severe change of the cantilever reference frequency in time.¹⁵ This drift is likely caused by thermal fluctuations of the AFM system, by an evaporation of the liquid or by stray excitations of

a)Present address: SmarAct GmbH, Schuette-Lanz-Strasse 9, 26135 Oldenburg, Germany.

b)URL:http://www.self-assembly.uni-mainz.de.

c)Present address: Department of Physics and Astronomy, The University of Utah, 115 South 1400 West, Salt Lake City, UT 84112, USA; Electronic mail: rahe@uni-mainz.de.

the surrounding environment. In principle, each of these is- sues can be addressed individually by a careful experimental design.3,4,9,16–18Second, finding a suitablefsetpoint for imaging in the repulsive regime can be delicate and imaging in this regime might significantly wear off the scanning probe tip. Third, imaging in liquids is typically performed in the repulsive tip-sample interaction regime. This is due to the fact that in the attractive regime the frequency shift signal does often not largely deviate from the noise level, even at the largest negative values. As a consequence, the attractive regime is hardly accessible. The latter statement is especially true when considering drift inf₀, easily causing absolute frequency drifts that are larger than thef(z) minimum. This possibly brings the feedback loop into an instable regime. Last, the amplitude spectrum usually resembles the well-known “forest of peaks,” where numerous resonances besides the cantilever resonance are apparent due to the environment.^19–21 This is- sue has been addressed by using direct actuation methods such as magnetic,²² photothermal,^16,23 and electrostatic^20,24 excitation.

Here, we present a new measurement mode where the tip-sample distance is adjusted such that imaging is always performed at the minimum of thef(z) curve. The existence of a minimum in thef(z) curve is a prerequisite for using this measurement mode. This mode is introduced as a promising strategy addressing the aforementioned challenges and pro- viding most practical solutions to them: First, it is immune against drift of the cantilever reference frequency as we regulate on thezderivative of thefsignal. Second, the setpoint for the distance feedback loop is well-defined and does not re- quire any adjustment, and third, it images the sample system in the overall attractive regime.

(3)

043707-2 Rodeet al. Rev. Sci. Instrum.85, 043707 (2014)

Imaging in the overall attractive regime is gentler than imaging in the repulsive regime. Consequently, we expect our measurement mode to reduce modifications of sensitive materials such as biological samples or other soft matter.

II. PRINCIPLE

The main measurement signal in FM NC-AFM is the frequency shiftf, defined byf=f−f₀.²⁵Here,f₀is the frequency of the cantilever oscillating without any tip-sample interaction, which changes tofwhen the tip is interacting with the sample. The frequency shiftfis related to the tip-sample interaction forceF_ts by convolving the force with a weight- ing function resembling the cantilever oscillation.²⁶ The frequency shiftf(z) along the tip-sample distancezusually fol- lows a curve qualitatively similar to the interaction force as depicted in Fig.1(solid green curve): Far away from the surface in the long-range regime, the interaction is basically zero.

Upon approach, at first long-range attractive van der Waals and electrostatic interactions are the dominant interactions, leading to a negative shift inf. A minimum is passed when repulsive interactions become more pronounced upon reduc- ing the tip-sample distance and, finally, repulsive interactions dominate, typically when the frequency shift is positive.²⁷

In Fig. 1, the derivative f(z) (dashed orange curve) is presented in addition to the f(z) curve (solid green).

The derivative exhibits a maximum at the inflection point of thef(z) curve and, most importantly, has its root at the f(z) minimum position. The method described here uses this derivative as the input signal for the topography feedback loop. When keeping thefsetpoint at zero, the topography signal will map an isosurface off(z)=min, i.e., the vertical position of thef(z) minimum for each lateral point. This specific position along thef(z) curve is usually inaccessible with a feedback relying on a monotonic behavior due to the change in sign of the slope in thef(z) curve.

Experimentally, the derivative is directly accessible using a well-known lock-in principle: thezpiezo signal is modulated with frequency f_mod and amplitude A_mod. The amplitude and phase of the resulting oscillation in fare then measured using a lock-in amplifier. The technical implementation is presented in Sec.III.

Modulation techniques of the Z position have been used before to rapidly discriminate between different chemical species from the slope off(z) curves.²⁸Furthermore, Z modulation has been used to quickly recover the nonlinearf(z)

FIG. 1. Schematicf(z) interaction curve for FM NC-AFM experiments (solid green) and corresponding derivativef(z) curve (dashed orange). The trajectory of the tipz(t) and the resultingf(t) signal are included in solid red and orange, respectively.

curve from measuring the higher harmonics in the frequency shift signal.²⁹

III. IMPLEMENTATION

For implementing our “dip-df” mode, where the tip- sample distance is regulated to the minimum dip of thef(z) curve, an oscillating signal with amplitude A_mod and frequency f_mod is added to the high-voltagez signal from the scan controller. This leads to a modulation of the tip-sample distance, which, in turn, results in a modulation of the frequency shiftf.²⁹As depicted in Fig.1, this oscillation along thezdirection results in an oscillation of thefsignal if the slope of thef(z) curve differs from zero, i.e., within the sample range. The amplitude of this oscillation in thefchannel is dependent on the slope of the f(z) interaction and ap- proaches zero at thef(z) minimum position. As the phase between thezoscillation signal and thefoscillation changes by 180^◦when passing thef(z) minimum, in addition the sign of the slope is readily available. Technically, the amplitude including the 180^◦phase shift when passing the minimum is easily detected using the in-phase signal of a lock-in amplifier.

Fig.2depicts the technical implementation of the dip-df method. Only two changes are necessary compared to a standard FM NC-AFM setup: First, a sinusoidal signal is added to thezsignal generated by the scan controller and, second, the in-phase (X) signal of the lock-in amplifier is fed into the topography feedback loop as input signal. Thefsignal from the PLL is then used as the input signal for the lock-in amplifier.

The signal summation is realized by adding the sinusoidal signal from a frequency generator to the scan controller signal. We used a mass-decoupled concept for the low- noise summation of low-voltage to high-voltage signals as described in Ref.30.

As PLL and lock-in amplifier we used an HF2 device from Zurich Instruments (Zurich, Switzerland). For the z modulation, a frequency in the range off_mod=6–8 kHz and an amplitude of aboutAmod=100 mV were used. This amplitude corresponds to a physical amplitude of about 1.5 Å using the calibration for the herein used modified Bruker Mul- timode V atomic force microscope.¹³ The PLL was set to a bandwidth slightly larger than f_mod, while the response of the z feedback loop was set significantly slower. The time constant of the lock-in amplifier was in the order of 30μs.

For regular FM NC-AFM experiments, an easyPLL plus (Nanosurf, Neuchâtel, Switzerland) controller and detector with a bandwidth of 1300 Hz was used in parallel for practical reasons. The reference frequency was determined from the excitation spectrum far away from the sample surface.

The dip-df method implementation and all experiments were performed using a modified Bruker Multimode V AFM, optimized for low-noise performance in the FM NC-AFM mode.¹³ Gold coated p-doped silicon cantilevers (type PPP- NCH-AuD from Nanosensors, Neuchâtel, Switzerland) with typical frequencies of around 160 kHz in liquid were operated at amplitudes of around 1–2 nm. The microscope is enclosed by a home-built measurement chamber. The temperature of the entire compartment is controlled by This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

(4)

FIG. 2. Technical implementation of the dip-df AFM mode. Components additional to a standard FM NC-AFM setup are depicted in green: Lock-in amplifier (LIA), generator for the oscillation signal (fmodgen), and high-voltage summation circuit (+). The phase-locked loop (PLL) is set to a bandwidth larger than fmod.

current-regulated resistors, allowing for temperatures in the range of 30–50^◦C. The resulting temperature stability of this setup is about±0.5^◦C.¹³

As substrate, we used the calcite (1014) surface,³¹ the most stable cleavage plane of the most stable polymorph of calcium carbonate CaCO3. Pristine surfaces were created by cleaving a bulk crystal in air and immediately introducing it into the liquid cell. The liquid cell was filled with deionized (Milli-Q) water. Following this preparation routine allows for achieving atomic-resolution imaging of the calcite substrate using FM NC-AFM as has been demonstrated before.⁵

IV. DEMONSTRATION

Exemplary f(z) curves acquired on the CaCO3(1014) surface are reproduced in Fig.3. These curves present a sin- gle minimum where the dip-df approach can be applied in a straightforward manner. On calcite, recent experiments have revealed the different hydration layers on the surface,⁸leading to multiple minima in thef(z) curve. Under the assumption that the separation of the minima along zis larger than the modulation amplitudez_modand that the signal-to-noise ratio allows for a clear distinction of the multiple zero positions in f, we can speculate that the dip-df mode might even distinguish between these minima. In contrast, we expect to aver- age the substructure and lock to the global minimum by using large oscillation amplitudesz_mod. As mentioned before, the peak of the attractive regime can be very shallow compared to the noise level as is clearly visible. Especially when considering drift off0 in the order of a several Hz/min, the minimum is hardly accessible experimentally within the timespan necessary for imaging. Thus, imaging is usually performed in the steep regime of negative slope. Furthermore, we find from this curve a difference in height in the order of 5 Å between imaging at positive frequency shift and imaging at the minimum.

Although measuring in the repulsive regime might be neces-

sary to achieve atomic-scale resolution, it is also expected to lead to instabilities and potential damages on tip or sample.

Using regular FM NC-AFM in f feedback, we approach and image a CaCO₃(1014) surface on a large scale.

Figure 4(a) presents the topography image acquired in the negativef(z) slope regime at a setpoint of about+100 Hz.

After completing this image, thezmodulation is switched on while the height feedback loop is still engaged. The phase offset of the lock-in amplifier is adjusted such that the in-phase signal is maximized. Depending on the input sign of the distance feedback loop configuration, an inversion (phase shift of 180^◦) of the signal might be necessary. The tip is retracted after this adjustment, the distance feedback loop is frozen and its input signal is changed fromfto the lock-in in-phase signal. Thef(z) curve is constant at large tip-sample distances, resulting in a zero in-phase and amplitude signal of the lock-in amplifier. Consequently, in order to engage to the sample after reactivating the feedback loop, a small offset added to the

FIG. 3. Representativef(z) curves acquired on the CaCO3(1014) surface for different tip terminations and different surface sites. In most cases, the attractive regime is hardly accessible due to the small peakedness compared to the noise level. All curves have been shifted along the vertical axis to match zero atz=5 nm.

(5)

043707-4 Rodeet al. Rev. Sci. Instrum.85, 043707 (2014)

FIG. 4. (a) Regular FM NC-AFM mode using the frequency shiftfas input for the topography feedback loop. (b) Dip-df AFM mode using the derivation f(z) as input signal for the topography feedback loop with setpoint zero.

The resulting image, thus, represents the isoplane of minimumf. Both images were compensated for vertical thermal drift, scanner hysteresis, sample tilt, and tip changes by a line-by-line and second order polynomial cor- rection. The position of the line profile extracted from the frequency shift channel (see Fig.5) is marked by a black line. Parameters for both images:

512×512 pixel²at 1 line/s (forward and backward scan).

in-phase lock-in signal is usually necessary. After stabilizing the tip position close to the surface, this offset is set to zero for stabilizing the tip precisely at the minimum of thef(z) curve. We note that the intermediate maximum of thef(z) curve is not causing feedback instabilities and can easily be passed as we regulate on the zero position.

Figure4(b)presents the topography channel when operating in the dip-df mode. The topography now directly resembles the isosurface of thef(z) minimum position. The data acquired in the regular FM mode and the dip-df mode are acquired at the same sample position, the lateral movement is caused by drift. In both images, calcite step edges and an etch pit due to calcite dissolution in water are resolved.

By comparing the two topography images (see Fig.4), we observe a slight increase in the topography signal noise for the dip-df mode. Although the RMS noise in the topography signal can by itself already be subject to the feedback

FIG. 5. Averaged line profile extracted at the indicated position in Fig.4(b) from the regularfchannel (shown in the inset, see also Fig.4(b)). The horizontal axis has been rescaled to depict the elapsed time. A linear regres- sion directly reveals a drift of the cantilever reference frequencyf0of about 2 Hz/min.

loop characteristics, we especially note that the dip-df method operates in a conventionally not reachable interaction regime around thefminimum. Compared to the repulsive regime, the absolute forces are smaller around the minimum position, explaining the possibility for larger noise under the same ef- fective measurement conditions.

To illustrate the robustness of this technique against drift of the cantilever frequencyf0, we present in Fig.5a line profile extracted from thefchannel acquired simultaneously to Fig.4(b). A linear fit reveals a drift of about 2 Hz/min, which would severely hinder measuring in the attractive regime after a few minutes. We also note that the dip-df technique delivers a strategy to distinguish between drift along the spatialzaxis and the cantilever frequencyf0.

V. CONCLUSION

We presented a new AFM measurement mode, which allows for NC-AFM experiments at tip-sample distances corresponding to the f(z) minimum, resulting in a map of f =min. Especially when using FM NC-AFM in liquid environment, thisdip-dfmode is a helpful extension to the regular FM mode. It circumvents the problem of drift in the cantilever reference frequencyf₀ and allows for imaging in the attractive tip-sample interaction regime. We successfully im- aged the calcite CaCO3(1014) surface in this mode revealing step edges and etch pits.

Especially on soft or sensitive sample systems, we ac- count this mode to be beneficial compared to the regular repulsive FM NC-AFM mode in liquids due to reduced tip-sample interaction forces while imaging.

ACKNOWLEDGMENTS

We thank Christoph Marutschke, Holger Adam, and Steffi Klassen for their most helpful experimental assistance, Christopher Hauke for naming the method, and Sadik Hafi- zovic for most helpful support with the HF2 configuration.

1H.-J. Butt, B. Cappella, and M. Kappl,Surf. Sci. Rep.59, 1 (2005).

2C. Barth, A. S. Foster, C. R. Henry, and A. L. Shluger,Adv. Mater.23, 477 (2011).

3T. Fukuma, M. Kimura, K. Kobayashi, K. Matsushige, and H. Yamada, Rev. Sci. Instrum.76, 053704 (2005).

(6)

4T. Fukuma, K. Kobayashi, K. Matsushige, and H. Yamada,Appl. Phys.

Lett.87, 034101 (2005).

5S. Rode, N. Oyabu, K. Kobayashi, H. Yamada, and A. Kühnle,Langmuir 25, 2850 (2009).

6M. Ricci, P. Spijker, F. Stellacci, J.-F. Molinari, and K. Votchovsky,Lang- muir29, 2207 (2013).

7H. Imada, K. Kimura, and H. Onishi,Chem. Phys.419, 193 (2013).

8H. Imada, K. Kimura, and H. Onishi,Langmuir29, 10744 (2013).

9Y. Araki, K. Tsukamoto, N. Oyabu, K. Kobayashi, and H. Yamada,Jpn. J.

Appl. Phys.51, 08KB09 (2012).

10N. Kobayashi, S. Itakura, H. Asakawa, and T. Fukuma,J. Phys. Chem. C 117, 24388 (2013).

11S. Rode, R. Hölscher, S. Sanna, S. Klassen, K. Kobayashi, H. Yamada, W.

G. Schmidt, and A. Kühnle,Phys. Rev. B86, 075468 (2012).

12M. Schreiber, M. Eckardt, S. Klassen, H. Adam, M. Nalbach, L. Greifen- stein, F. Kling, M. Kittelmann, R. Bechstein, and A. Kühnle,Soft Matter9, 7145 (2013).

13S. Rode, R. Stark, J. Lübbe, L. Tröger, J. Schütte, K. Umeda, K. Kobayashi, H. Yamada, and A. Kühnle,Rev. Sci. Instrum.82, 073703 (2011).

14P. Rahe, R. Bechstein, and A. Kühnle,J. Vac. Sci. Technol. B28, C4E31 (2010).

15F. J. Giessibl,Rev. Mod. Phys.75, 949 (2003).

16H. Adam, S. Rode, M. Schreiber, K. Kobayashi, H. Yamada, and A.

Kühnle,Rev. Sci. Instrum.85, 023703 (2014).

17N. Umeda, S. Ishizaki, and H. Uwai,J. Vac. Sci. Technol. B9, 1318 (1991).

18G. C. Ratcliff, D. A. Erie, and R. Superfine,Appl. Phys. Lett.72, 1911 (1998).

19T. E. Schäffer, J. P. Cleveland, F. Ohnesorge, D. A. Walters, and P. K.

Hansma,J. Appl. Phys.80, 3622 (1996).

20K.-I. Umeda, K. Kobayashi, K. Matsushige, and H. Yamada,Appl. Phys.

Lett.101, 123112 (2012).

21X. Xu and A. Raman,J. Appl. Phys.102, 034303 (2007).

22W. Han, S. M. Lindsay, and T. Jing,Appl. Phys. Lett.69, 4111 (1996).

23A. Labuda, K. Kobayashi, Y. Miyahara, and P. Grütter,Rev. Sci. Instrum.

83, 053703 (2012).

24K.-I. Umeda, N. Oyabu, K. Kobayashi, Y. Hirata, K. Matsushige, and H.

Yamada,Appl. Phys. Express3, 065205 (2010).

25T. R. Albrecht, P. Grütter, D. Horne, and D. Rugar,J. Appl. Phys.69, 668 (1991).

26F. J. Giessibl,Phys. Rev. B56, 16010 (1997).

27P. Rahe, R. Bechstein, J. Schütte, F. Ostendorf, and A. Kühnle,Phys. Rev.

B77, 195410 (2008).

28Y. Sugimoto, T. Namikawa, M. Abe, and S. Morita,Appl. Phys. Lett.94, 023108 (2009).

29S. Kawai, S. Hafizovic, T. Glatzel, A. Baratoff, and E. Meyer,Phys. Rev. B 85, 165426 (2012).

30P. Rahe, J. Schütte, W. Schniederberend, M. Reichling, M. Abe, Y. Sugi- moto, and A. Kühnle,Rev. Sci. Instrum.82, 063704 (2011).

31P. Rahe, J. Schütte, and A. Kühnle,J. Phys.: Condens. Matter24, 084006 (2012).